From insulator to quantum Hall liquid at low magnetic fields

We have performed low-temperature transport measurements on a GaAs two-dimensional electron system at low magnetic fields. Multiple temperature-independent points and accompanying oscillations are observed in the longitudinal resistivity between the low-field insulator and the quantum Hall (QH) liquid. Our results support the existence of an intermediate regime, where the amplitudes of magneto-oscillations can be well described by conventional Shubnikov–de Haas theory, between the low-field insulator and QH liquid.

Figure 1

(Color online) Longitudinal resistivity ${\rho }_{xx}$ as a function of magnetic field $B$ for $V_g=-0.02\text{V}$ at various temperatures $T$. Four approximately $T$-independent points are indicated by arrows. The inset shows ${\rho }_{xx}\left(B\right)$ $\left(T=0.25\text{K}\right)$ and Hall resistivity ${\rho }_{xy}\left(B\right)$ at $T=0.25\text{K}$ (higher Hall slope at low $B$) and $T=1.6\text{K}$ (lower Hall slope at low $B$) for $V_g=-0.02\text{V}$.

Figure 2

$\Delta {\rho }_{\text{SdH}}/D\left(B,T\right)$ as a function of $1/B$ for $V_g=-0.02\text{V}$ and $V_g=-0.06\text{V}$. The full symbols denote the SdH amplitudes at $V_g=-0.02\text{V}$ when the temperature $T=0.25$, 0.52, 0.71, 0.90, 1.07, 1.30, and 1.60 K. The open symbols denote the amplitudes at $V_g=-0.06\text{V}$ when $T=0.25$, 0.32, 0.47, 0.61, 0.78, 0.93, 1.01, 1.22, and 1.37 K. The solid and dashed lines correspond to fits to $\Delta {\rho }_{\text{SdH}}/D\left(B,T\right)=C\text{exp}\left(-\pi /\mu B\right)$, where $C$ is a constant independent of $B$ and $T$ when $V_g=-0.02\text{V}$ and $-0.06\text{V}$, respectively. The inset shows $\text{ln}\Delta {\rho }_{\text{SdH}}$ as a function of $1/B$ at $T=0.25\text{K}$ when $V_g=-0.02\text{V}$. The solid line corresponds to a fit to $\Delta {\rho }_{\text{SdH}}=C\text{exp}\left(-\pi /\mu B\right)$.

Figure 3

${\rho }_{xx}\left(B\right)$ for $V_g=0$ at various $T$. Six approximately $T$-independent points are indicated by arrows.

Figure 4

${\rho }_{xx}\left(B\right)$ for $V_g=-0.04\text{V}$ at various $T$. Two crossing points are indicated by arrows and the crossing point at the highest $B$ is indicated by a vertical solid line.

Figure 5

Traces of ${\rho }_{xx}\left(B\right)$ for $V_g=-0.06\text{V}$ at different $T$. The transition field $B_c$ is indicated by a vertical solid line. Inset (a) shows a zoom-in of ${\rho }_{xx}$ near the transition field $B_c$ at various temperatures. From top to bottom at $B=0.9\text{T}$, $T=0.25$, 0.32, 0.47, 0.61, 0.78, 0.93, 1.01, 1.22, and 1.37 K. Inset (b) shows ${\rho }_{xx}\left(B\right)$ for $V_g=-0.117\text{V}$ at various $T$.